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Math 10
4.2 Notes
Exponent Laws
Exponent Laws tells us what to do with the exponents (if we are asked
to multiply or divide powers). L U\wS ose. j us+ -h ('(1< S o..V-<!.{S )
There are 6 Exponent Laws that you must know.... S\)we ~ ov\ ..t- net ve.+0 \JJ (l t- ~ OLA t- \ ()~
. CotlculOl-h'O(1\S .#1 - Multiplying powers with the same base
. \ \0.6
~if +2- ~Ex: [(2x)4(2x)2]= ( ~:L ~(~~)
LJ L-J
ba~~
(95)(9-2) =5 + l-2.) q3Ex: 9 -~.
#2 - Dividing powers with the same base
a=l=-O·Ex: 75 =
72
Same as:
1!:)-2.. - 13
G-~~-~---:3)~If ~ ;f:¥~/t-(o-3
)L
I\... o. ~.o..~V'I()+ eq..uu \2<.,,0 .
Ex: (2X)3 =(2xr2
t bo.>.t \ ~ ·a){
* *Another way to solve this question, is to write (2xr2 as apositive exponent:
~( c?- ~ )
Exponent Law Worksheet: Do Part 1
,- .
#3 - A Power Raised to a Power
Ex: (23)3 = :1303"" ;) q
Same as: (~'f-?- ~ ?- ) ( ~ 'f- ?- " ~ ') ( ~ 'f.. ;l'f- ~) .~
Ex: (52)3 = (:) ) -a"'3, ~ 5 (0
( L\-)(3) (- ~) _ IJ - l,Ex: [(4X)2]3 = ~1
( Lt 1-- /' 3 '" (+)(.) 10
The last two laws deal with situations where you do NOT have theo.
same bases, But we have already seen these rules before l~-. - -e.'i. ::
IL\0Ex: r 21\0=
l31
Ex: [~ r =
#4 - Power of a Quotient
[~~" = :nn .L-_---b~~~D -----'U if __.: ~. 4..
~ ~ _ Y- Ex: rv:14 = ,~ ~;)?-- -9 L 2xJ ~ ~ >( '\ \ (0 ')( 4
~~->, \)04G'· -tv ev\-K( an
e.x txJ'f\..tn+ Of\ "I tJvt ('Cct \ (ct \ ut-\1) (' ~
J.4: :l [b] ~ ~ lb
~(£1q~\6
I
\R5
#5 - Power of a Product
(ab)-DJ= an'bn
{\J{~-thi~ .' (\$\ de \?rttc\.u-\ s i-S (~~~G~ to expo()R()t
mU. \t~P~ ¥nVD~h2 f}a~,.., i\ 2-
Ex: (2x) = (j.. "or.. _ \" ~
( ~X)( ~'X) ~3 '3> ~J j = ~1-j~3 lq)(-3) _-3 -\ ~X~~t =-'1~
m'-' \-hp'j
(pow -ov vll:~d ~ OtpouJ-t()
Ex: (3y)3 =
10'1 _
::i....."3(j 12-
Summary: EXPONENT LAWS
Multiplying powers with the same base (am )(an) rn+n= aDividing powers with the same base am m-n= a
an
A Power Raised to a Power (am t = am-n
Power of a Quotient n n~ = ~b bn
Power of a Product (ab)" = an·bn
Zero Exponent aD -1
f\Nt) •. 'O--n \'" ---'0.-("\1l:Jo.-r;\le.., \ 0.-(\-e.XpOV\ t f\-\- S : (),-n
Applying More than 1 Law:
Exf~:l3= (J ~-~)-3 _
t c\.ea\ w-\+\\~P(){\-e(\t-S \0S\cU bitt lkits '
EX:~~3 =
[ -l-l\-+,,]-3
[-c-J-3(-3; -3
~ ['(\1\ \hpl:)IL J- 2.. 1--1--1")-1,----, L\
L-.-~-\2.. . \0 cJ..!
::Lj = L~
Exponent law Worksheet: Do Part 2
Text Book: p. 169 #4 and 5